Cellular communications system receivers

ABSTRACT

An impulse response matrix of a received signal in a TDMA communications system is approximated using a plurality of indirect variables of a linear complex vector. The indirect variables are used for synchronizing to the received signal and for tracking and frequency offset estimation during successive samples of the received signal, the samples being equalized in dependence upon the indirect variables. A demodulated signal is derived from the equalized received signal samples. Individual synchronization and tracking units, and a single equalizer, can be provided for a two-antenna receiver. Tracking errors can be used to adapt a parameter of the equalizer to reduce interference in the received signal.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/RU00/00181, filed 16 May 2000.

This invention relates to cellular communications system receivers, andis particularly concerned with such receivers for use in mobile radiosystems, such as TDMA. (time division multiple access) systems.

BACKGROUND

It is well known that it is necessary in a receiver of a cellular mobileradio system to recover each communicated signal under varying andchallenging conditions. These conditions include, for example, thepresence of multi-path signals and fading resulting in lowsignal-to-noise ratio (SNR), the presence of strong co-channelinterfering (CCI) signals, and Doppler effects due to relative movementof the signal transmitter and receiver, as well as typical constraintsdue to factors such as limited channel bandwidth and equipmenttolerances. In the case of a TDMA system, it is necessary to recover thetiming and synchronize to the time division multiplex (TDM) frames andtime slots of a received digital communications signal. It is alsodesirable to provide the receiver with the least possible cost andcomputational complexity.

International Publication Number WO 97/08867 dated division multipleaccess) systems. Mar. 6, 1997, in the name of Northern Telecom Limitedand entitled “Timing Recovery And Frame Synchronization In A CellularCommunications System”, discloses a method of timing recovery in whichindirect variables of a linear complex vector are estimated using amaximum likelihood criterion in order to recover sampling delay andhence the timing and frame synchronization of the received signal.

There remains a need to provide improved receivers for cellularcommunications systems.

SUMMARY OF THE INVENTION

According to one aspect of this invention there is provided a method ofprocessing samples of a received signal to produce a demodulated signal,comprising the steps of: representing an impulse response matrix for thereceived signal using a plurality of indirect variables of a linearcomplex vector; synchronizing to the received signal samples independence upon the indirect variables; tracking the indirect variablesfor successive received signal samples; equalizing the successivereceived signal samples in dependence upon the tracked indirectvariables; and producing the demodulated signal in response to theequalized received signal samples.

Thus in accordance with this method the indirect variables trackvariations in distortions, such as delay, fading, and phase distortions,and their use is extended to signal processing steps for producing thedemodulated signal, thereby facilitating an improved performance of theentire receiver of a communications system.

The received signal may in particular be a signal of a TDMAcommunications system, and the step of synchronizing to the receivedsignal samples can comprise matched filtering the received signalsamples to produce the plurality of indirect variables, and determininga maximum of a function of the indirect variables to determinesynchronization. In a particular embodiment of the invention describedbelow, there are four indirect variables and said function is a functionof only two of the indirect variables.

The step of tracking the indirect variables for successive receivedsignal samples can comprise recursively filtering initial values of theindirect variables, established during the synchronizing step, independence upon the successive received signal samples, and can alsocomprise a step of estimating frequency offset in dependence upon thesuccessive received signal samples. This enables the tracking to beeffective over time slots in a TDMA system operating at highfrequencies, for example 2.4 GHz, despite rapid changes due to Dopplereffects arising from relative movement between a transmitter and areceiver of the received signal.

The step of equalizing the successive received signal samples cancomprise adaptively changing an equalizer parameter in dependence upontracking errors for successive received signal samples to reduceco-channel interference with the received signal.

The method can advantageously be applied in a dual antenna receiverarrangement in which said indirect variables are produced and trackedindividually in respect of samples of a received signal from each of twospaced antennas, received signal samples from the two antennas beingcombined and equalized in dependence upon a combination of the indirectvariables in respect of the two antennas.

Another aspect of the invention provides apparatus for producing ademodulated signal from samples of a received signal, comprising: asynchronization unit responsive to the received signal samples forproducing a linear complex vector comprising a plurality of indirectvariables having initial values corresponding to a synchronized state; atracking unit responsive to the initial values of the indirect variablesand to the received signal samples to produce tracked values of theindirect variables for successive received signal samples; an equalizerresponsive to the tracked values of the indirect variables to equalizesuccessive received signal samples; a feedback path from the equalizerto the tracking unit to facilitate producing the tracked values of theindirect variables by the tracking unit; and a demodulator responsive tothe equalized received signal samples to produce a demodulated signal.

The synchronization unit can comprise a plurality of finite impulseresponse filters for matched filtering of the received signal samples toproduce the plurality of indirect variables. The tracking unit cancomprise a recursive filter for recursively filtering the indirectvariables in dependence upon the successive received signal samples.

The apparatus can also include a frequency offset estimator coupled tothe tracking unit for modifying the tracking of the indirect variablesin accordance with estimated frequency offset in dependence upon thesuccessive received signal samples.

For reducing co-channel interference, the apparatus advantageouslyincludes a unit, responsive to tracking errors determined by thetracking unit for successive received signal samples, for estimating aninterference correlation matrix to adaptively change a parameter of theequalizer.

The apparatus can include respective synchronization and tracking unitsfor samples of a received signal from each of two spaced antennas, theequalizer being responsive to the tracked indirect variables for bothantennas to combine and equalize the received signal samples from thetwo antennas.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be further understood from the following descriptionby way of example with reference to the accompanying drawings, in which:

FIG. 1 schematically illustrates a dual antenna TDMA cellular radiosystem receiver using indirect variables in accordance with anembodiment of the invention;

FIG. 2 schematically illustrates indirect variable synchronization andframe synchronization units of the receiver of FIG. 1;

FIG. 3 schematically illustrates a linear indirect variable equalizer ofthe receiver of FIG. 1;

FIG. 4 schematically illustrates indirect variable tracking, frequencyoffset estimation, and KD units of the :receiver of FIG. 1;

FIG. 5 schematically illustrates a hard limiter of the receiver of FIG.1;

FIG. 6 schematically illustrates an optional interference correlationmatrix estimator of the receiver of FIG. 1; and

FIG. 7 schematically illustrates a single antenna TDMA cellular radiosystem receiver using indirect variables in accordance with anotherembodiment of the invention.

DETAILED DESCRIPTION

Embodiments of the invention are described below in the context of areceiver for use in a TDMA cellular system compatible with EIA/TIAdocument IS-54-B: Cellular System Dual Mode Mobile Station—Base StationCompatibility Standard (Rev. B) and later documents referred to asIS-136 and IS-136+, minimum performance standards for which arespecified in a document referred to as IS-138. For brevity, this isreferred to below simply as the TDMA system and the IS-54 standard.However, the principles of the invention are also applicable to otherTDMA systems and to other types of communications system receiver.

Such a TDMA system requires a receiver having a high performance foroperation in various radio channel conditions which include a frameduration of 20 ms, a channel bandwidth of 30 kHz, a multi-path delayspread of up to 42 μs (one TDMA symbol) with equal powers of themulti-path signals, Doppler frequency up to 200 Hz, and the presence ofup to 3 strong co-channel interference signals. The receiver is desiredto provide the best possible sensitivity and multi-path fadingreception, despite these conditions, with the least possible computationcomplexity and cost.

It is well known to enhance reception of radio channels subject tofading by using two (or more) spaced antennas whose respective receivepath signals are combined in a desired manner, and the first embodimentof the invention described below relates to a dual antenna receiverarrangement. However, the invention is also applicable to a singleantenna receiver, as described later below.

Despite the use of two antennas, a design of receiver for operation inthe various conditions outlined above presents a significant challenge.As indicated above, one such design described in publication WO 97/08867makes use of indirect variables to recover timing and framesynchronization of the received signal.

As described in that publication, each component of an impulse responsematrix G(τ) is approximated by a linear combination, plus a constantterm, of a pair of functions φ₁(τ) and φ₂ (τ). Several examples offunction pairs are given. This leads to introduction of a variable Φ_(n)which is a 3-dimensional complex vector constituted by the transpose ofthree indirect variables φ_(1,n), φ_(2,n), and φ_(3,n), which are usedin the processes of timing recovery and frame synchronization. Therecovered timing and synchronization parameters are then used inconventional manner for deriving the content of the received signals.

The present invention also uses indirect variables, but does not merelyuse them for timing recovery and frame synchronization. Rather, theinvention recognizes that parameters such as the sample timing and framesynchronization are only means to the end of recovering the content ofthe received signal, and that these parameters do not necessarilyprovide any value for themselves. Instead, the invention makes use ofindirect variables substantially throughout the entire receiver, andthen recovers the content of the received signal from the indirectvariables at the demodulator. This facilitates achieving an improvedreceiver performance. In particular, as described further below, theindirect variables can be used in tracking channel changes, Doppler andother frequency offsets, providing equalization, and also in reducingthe adverse effects of co channel interference.

Referring to FIG. 1, which illustrates a dual antenna TDMA systemreceiver using indirect variables in accordance with an embodiment ofthe invention, two spaced antennas 10A and 10B are coupled to respectivereceiver front end units 12A and 12B, each of which includes a radiofrequency receiver, down converter, sampler, and analog-to-digitalconverter of known form to provide at its output digital complex signalsamples Y_(n) ^(A) and Y_(B) ^(B), the subscript n denoting the samplenumber and the superscript A or B denoting the antenna. These signalsamples are supplied to a respective one of two indirect variable (IN.VAR.) synchronization units 14A and 14B, to a respective one of twoindependent variable tracking units 16A and 16B, and to a linearindependent variable equalizer 18 of the receiver of FIG. 1.

The receiver of FIG. 1 also includes, commonly for the signals of thetwo antennas, a frame synchronization unit 20, a frequency offsetindirect variable estimator 22, a hard limiter 24, a KΦ calculation unit26, and a demodulator 28. Signal connection among these various units ofthe receiver are shown in FIG. 1 and are further described below. Inaddition, the receiver can optionally include an interference(correlation matrix (ICM) estimation unit 30 which is shown with itsconnections in dashed lines in FIG. 1.

In order to understand the further description below, it is expedient toconsider a mathematical background which leads to such understanding.This consideration is for a two-path signal model in an IS-54 TDMAsystem, in which as is well known signals are communicated usingπ/4-shifted DQPSK (differential quadrature phase shift keyed) signalsymbols in non-overlapping time slots each of which comprises datasymbols, known synchronization symbols (sync word), and known CDVCCsymbols. The known symbols, in particular the sync word, facilitatedetermination and tracking of parameters of the signal received duringthe time slot, these parameters including for example carrier phasewhich can vary during the lime slot.

With sampling as is usual at twice the clock frequency, a discreteobservation model for the received signal samples has the form:$\begin{matrix}\begin{matrix}{y_{i} = {{\sum\limits_{k = 0}^{M}{u_{i}^{1}s_{k}{g\left( {\frac{i\quad T}{2} - \tau_{1} - {k\quad T} - \frac{T}{2}} \right)}}} +}} \\{{\sum\limits_{k = 0}^{M}{u_{i}^{2}s_{k}{g\left( {\frac{i\quad T}{2} - \tau_{2} - {k\quad T} - \frac{T}{2}} \right)}}} + \eta_{i}}\end{matrix} & (1)\end{matrix}$where Y_(i) is the complex observation sample, i denotes the samplenumber from 1 to 2N+1 in the observed data sequence, S_(k) are the knowncomplex symbols in the sync word of M symbols,$u_{i}^{m} = {\sqrt{P_{i}^{m}}{\exp\left( {j\psi}_{0}^{m} \right)}}$are unknown complex amplitude-phase multipliers for the differentindependently fading paths m=1 and m=2, the samples i on each path mhaving power p_(i) ^(m) and the average power of each path being halfthe average signal power, T is the symbol spacing or clock frequencyperiod, τ₁ and τ₂ are unknown delays of the two paths, g(t) is theimpulse response of concatenated transmitter and receiver filters, givenby:${g(t)} = {\left( \frac{\sin\left( {\pi\quad{t/T}} \right)}{\pi\quad{t/T}} \right)\left( \frac{\cos\left( {\alpha\quad\pi\quad{t/T}} \right)}{\left( {1 - \left( {2\alpha\quad{t/T}} \right)^{2}} \right)} \right)}$where α is the filter roll-off coefficient, and η_(i) is a noisesequence of complex Gaussian random variables with zero mean, variance2σ_(η), and correlation function 2σ_(η)g(((i-j)T)/2) between two randomvariables η_(i) and η_(j).

The channel model of Equation (1) can be written in the form:$\begin{matrix}\begin{matrix}{y_{i} = {{\sum\limits_{k = 0}^{M}{U_{i}^{1}{\overset{\sim}{s}}_{k}{g\left( {\frac{i\quad T}{2} - \tau_{1} - {k\quad T} - \frac{T}{2}} \right)}}} +}} \\{{\sum\limits_{k = 0}^{M}{U_{i}^{2}{\overset{\sim}{s}}_{k}{g\left( {\frac{i\quad T}{2} - \tau_{2} - {k\quad T} - \frac{T}{2}} \right)}}} + \eta_{i}}\end{matrix} & (2)\end{matrix}$where U_(i)^(m) = u_(i)^(m)s_(M)are the amplitude-phase multipliers during the sync word and {tilde over(S)}_(k)=S_(k)(S_(M))′ are transformed symbols of the sync word.Assuming that the amplitude-phase multipliers are constant during thesync word, then Equation (2) can be rewritten in matrix form as:$\begin{matrix}{Y_{n} = {{{G\left( \tau_{1} \right)}S\quad U_{n}^{1}} + {{G\left( \tau_{2} \right)}S\quad U_{n}^{2}} + H_{n}}} & (3)\end{matrix}$where Y_(n)=[y_(2n−1) y_(2n) . . . y_(2n+2N−2) y_(2n+2N−1)]^(T) is a(2N+1)-dimensioned observation vector, H_(n)=[η_(2n−1)η_(2n) . . .η_(2n+2N−2)η_(2n+2N−1)]^(T) is a (2N+1)-dimensioned vector of correlatednoise samples, S=(s_(m))′[s₀s₁. . . s_(M−1)s_(M)]^(T) is an(M+1)-dimensioned vector of known symbols, and G(τ) is the impulseresponse matrix given by: ${G(\tau)} = \begin{bmatrix}{g\left( {- \tau} \right)} & {g\left( {{- \tau} - T} \right)} & \ldots & {g\left( {{- \tau} - {MT}} \right)} \\{g\left( {{- \tau} + {T/2}} \right)} & {g\left( {{- \tau} - {T/2}} \right)} & \ldots & {g\left( {{- \tau} + {T/2} - {MT}} \right)} \\{g\left( {{- \tau} + T} \right)} & {g\left( {- \tau} \right)} & \ldots & {g\left( {{- \tau} - {\left( {M - 1} \right)T}} \right)} \\\ldots & \ldots & \ldots & \ldots \\{g\left( {{- \tau} + {NT}} \right)} & {g\left( {{- \tau} + {\left( {N - 1} \right)T}} \right)} & \ldots & {g\left( {{- \tau} + {\left( {N - M} \right)T}} \right)}\end{bmatrix}$According to the IS-54 standard,τ_(i)ε(−L _(pr) T/2;L _(pr) T/2) i=1,2|τ₁−τ₂ <Twhere L_(pr) is the number of sample spacings in an uncertainty range ofdelay, abbreviated below to L. With this uncertainty range determined tobe L=2 (path delays within two sampling intervals), then to ensure thatthe sync word symbols are all within an observation set the aboveimpulse response matrix must be increased by two initial rows and twofinal rows, so that with N=M it becomes a matrix with 2M+5 rows and M+1columns with components G_(ij)=g(−τ+(i−1−L)T/2−(j−1)T) where i is a rowindex from 1 to 2M+5 and j is a column index from 1 to M+1.

In publication WO 97/08867 an approximation g(τ+iT2)≡a_(1,iφ1)(τ)+a_(2,iφ2)(τ)+a_(3,i)i=. . . −2, −1,0,1,2, . . . or, inmatrix form, G(τ)≡A_(1φ1)(τ)+A_(2φ2) (τ)+A₃ is used for a single pathchannel to approximate the impulse response matrix G(τ), where a_(1,i),a_(2,i), and a_(3,i) are approximation coefficients and A₁, A₂, and A₃are approximation matrices with these coefficients. This approximationis reasonable for values of the variable τ within the interval [−T/2;T/2], but is not sufficient for two paths for which, with framesynchronization established, the uncertainty range is still [−3T/2;3T/2]. A good accuracy with this greater interval has been found withfour terms, i.e.:g(τ+iT/2)≡a _(1,iφ1)(τ)+a _(2,iφ2)(τ)+a _(3,iφ3)(τ)+a _(4,iφ4)(τ)i=. . .−2, −1, 0, 1, 2, . . .or G(τ)≡A _(1φ1)(τ)+A _(2φ2)(τ)+A _(3φ3)(τ)+A _(4φ4)(τ)  (4)

Various approximation functions can be used to provide a desiredapproximation accuracy, and the invention is not limited to anyparticular set of approximation functions. As one example, theapproximation functions may be:φ₁(τ)=sin (πτ/2T)φ₂(τ)=cos (πτ/2T)φ₃(τ)=sin (πτ/4T)φ₄(τ)=cos (πτ/4T)

As another example, the approximation functions may be:φ₁(τ)=g(τ)φ₂(τ)={tilde over (g)}(τ)φ₃(τ)=−1.22 g(τ)+g(τ/2)φ₄(τ)=−{tilde over (g)}(τ)+1.41 {tilde over (g)}(τ/2)where {tilde over (g)}(τ) is the Hilbert transform of the function g(t).These approximation functions provide a signal-to-approximation noiseratio of about 30 dB in a range of τ from −T to T. As can beappreciated, a preferred set of approximation functions, and the numberof functions in the set, depends on the desired approximation accuracy(signal-to-approximation noise ratio) and directly affects the resultingcomplexity of implementing the approximation functions in the receiver.

Because the difference in delays between the two paths is not more thanone symbol spacing interval, Equation (3) above can be rewritten, usingthe approximation functions, in the form:Y _(n) =A ₁ S(φ₁(τ₁)U _(n) ¹+φ₁(τ₂)U _(n) ²)+A ₂ S(φ₂(τ₁)U _(n)¹+φ₂(τ₂)U _(n) ²)+A₃ S(φ₃(τ₁)U _(n) ¹+φ₃(τ₂)U _(n) ²⁾ +A ₄ S(φ₄(τ₁)U _(n) ¹+φ₄(τ₂)U _(n)²)+H_(n)   (5)

If a 4-dimensioned vector Φ_(n) of indirect variables is defined by:Φ_(n)≡(φ_(1,n), φ_(2,n), φ_(3,n), φ_(4,n))whereφ_(i,n)=φ_(i)(τ₁)U_(n) ¹+φ_(i)(τ₂)U _(n) ² i=1,2,3,4  (6 )are the indirect variables, then the model of Equation (5) can beexpressed in the form:Y _(n) =BΦ _(n) H _(n)  (7)where B=[(A₁S)(A₂S)(A₃S)(A₄S)] is a known matrix because A₁ to A₄comprise fixed coefficients and S is the known sync word.

In this context, in the receiver of FIG. 1 the indirect variablesynchronization units 14A and 14B serve to produce initial values Φ₀^(A) and Φ₀ ^(A) respectively of the indirect variable vector Φ_(n) forsynchronization, and the indirect variable tracking units 16A and 16Bserve, in conjunction with the frequency offset indirect variableestimation unit 22, to track the indirect variable vector Φ_(n)throughout a time slot to produce tracked values Φ_(n) ^(A) and Φ_(n)^(B) respectively. The linear indirect variable equalizer 18 comprises aKalman filter which is controlled by the tracked values Φ_(n) ^(A) andΦ_(n) ^(B) of the indirect variable vector to combine and recursivelyfilter the received signal samples Y_(n) ^(A) and Y_(n) ^(B), therebyproducing a received and equalized signal vector S_(Θ,n). This vector islimited by the hard limiter 24, from the output of which the KΦcalculating unit produces a feedback control signal K_(Φ,n) for thetracking units and the demodulator 28 produces a demodulated signal onan output line 32 of the receiver. The various units of the receiver arefurther described below.

FIG. 2 illustrates one form of the indirect variable synchronizationunit 14A (the unit 14B is similar) and one form of the framesynchronization unit 20, for producing the initial value Φ₀ ^(A) forsynchronization. The unit 14A comprises four finite impulse response(FIR) filters (FIR-1 to FIR-4) 40 which are supplied with the receivedsignal samples Y_(n) ^(A), a calculation unit 42, a delay line 44comprising delay elements each providing a delay of one symbol spacinginterval T, and a selector 46. The frame synchronization unit 20comprises a combiner 48, a delay line 50, and a maximum detector 52.

In order to simplify matrix inversion, the model of Equation (7) isdivided into even and odd sample sets so that the model can be expressedas:Y _(n) ^(odd) =B _(odd)Φ_(n) +H _(n) ^(odd) Y _(n) ^(even) =B_(even)Φ_(n) +H _(n) ^(even)and, because B is a known matrix, the indirect variable vector can beinitially determined by a matched filtering represented by:Φ_(n) ^(odd)=(B _(odd) ^(T) B _(odd))⁻¹ B _(odd) ^(T) Y _(n) ^(odd)Φ_(n) ^(even)=(B _(even) ^(T) B _(even))⁻¹ B _(even) ^(T) Y _(n) ^(even)in which the first three terms on the right-hand side of each equationcan be pre-calculated and stored. It is observed that here and below thevarious signal processing operations produce results which are estimatesrather than the precise values of the respective signals. In FIG. 2, theFIR filters 40 perform this matched filtering function, the filtersFIR-1 and FIR-3 corresponding to the first and third rows respectivelyof the matrix (B_(odd) ^(T)B_(odd))⁻¹B_(odd) ^(T)Y_(n) ^(odd) and thefilters FIR-2 and FIR-4 corresponding to the second and fourth rowsrespectively of the matrix (B_(even) ^(T)B_(even))⁻¹B_(even) ^(T)Y_(n)^(even).

Consequently, the outputs of the FIR filters 40, which are supplied toinputs of the delay line 44, constitute the indirect variable vectorΦ_(n) in accordance with the above model, but its synchronization, i.e.the value n which provides a reference timing point, is not yetdetermined. This is determined as described below using, for simplicity,only the first two of the approximation functions described above, theoutputs of only the filters FIR-1 and FIR-2 being supplied to thecalculation unit 42, which calculates and produces at its output a valuemodΦ_(n). The calculation carried out by the unit 42 is dependent uponthe particular approximation functions which are used as describedabove. For the functions Φ₁(τ)=g(τ) and Φ₂(τ)={tilde over (g)}(τ)referred to above, for example,${{mod}\quad\Phi_{n}} = \frac{\left\lbrack {{{\varphi_{2}\left( \tau_{n} \right)}\phi_{2,n}} + {{\varphi_{1}\left( \tau_{n} \right)}\phi_{1,n}}} \right\rbrack^{T}\left\lbrack {{{\varphi_{2}\left( \tau_{n} \right)}\phi_{2,n}} + {{\varphi_{1}\left( \tau_{n} \right)}\phi_{1,n}}} \right\rbrack}{{\varphi_{2}\left( \tau_{n} \right)}^{2} + {\varphi_{1}\left( \tau_{n} \right)}^{2}}$where$\tau_{n} = {\frac{2}{\pi}\quad{real}\quad\left( {{atan}\left( \frac{\phi_{2,n}}{\phi_{1,n}} \right)} \right)}$and the calculation unit 42 calculates modΦ_(n) accordingly.

The values modΦ_(n) ^(A) and Φ_(n) ^(B) thus produced for the two pathsA and B are combined by the signal combiner 48 in the framesynchronization unit 20 to provide for frame alignment of the signalsfrom the two antennas, and the output of the signal combiner is suppliedto the delay line 50 having a length corresponding to the observationwindow of the received signal samples. The maximum detector 52determines the value n corresponding to a maximum one of the outputs ofthe delay line 50, thereby determining synchronization, and suppliesthis to the selector 46 in the unit 14A. The selector 46 selects fromthe delay line 44 the corresponding indirect variable vector Φ_(n) andsupplies this to its output as the initial indirect variable vector Φ₀^(A).

One form of the linear indirect variable equalizer 18 is illustrated inFIG. 3 and comprises a Kalman filter including signal combiners 60 and62, multipliers 64 and 66, and a delay element 68, and an arrangementfor determining filter parameters including calculation units 70, 72,74, and 76 and a delay element 78. The arrangement and operation of theequalizer will be further understood from the following description.

With prediction of estimates to an n-th step at the step n-L, the Kalmanfilter in FIG. 3 can be seen to provide its output S_(Θ,n) in accordancewith:

 S _(Θ,n) =A _(n) S _(n−1) +K _(S,n)(y _(n) −G(Φ_(n/n−L))(A _(n) S_(n−1)))  (8)

where K_(s,n) is a Kalman filter gain given by:K _(S,n) =[V _(S,n/n−1) G(Φ_(n/n−L))]G(Φ_(n/n−L))′[V _(S,n/n−1)G(Φ_(n/n−L))]+V _(η,n))⁻¹V _(S,n/n−1) =A _(n) V _(S,n−1) A _(n) ^(T) +V _(ξ,n)  (9)V _(S,n) =V _(S,n/n−1) −K _(S,n) [V _(S,n/n−1) G(Φ_(n/n−L))]where the terms of these equations can be understood from the followingdescription.

Extending a single antenna representation for the case of two antennasand hence two sampled signals, ${y_{n} \equiv \begin{bmatrix}y_{n}^{A} \\y_{n}^{B}\end{bmatrix}} = {{\begin{bmatrix}{G\left( \Phi_{n}^{A} \right)} \\{G\left( \Phi_{n}^{B} \right)}\end{bmatrix}S_{n}} + \begin{bmatrix}\eta_{n}^{A} \\\eta_{n}^{B}\end{bmatrix}}$where the last matrix represents equivalent noise including indirectvariable errors. This noise has the covariance matrix:${V_{\eta} = \begin{bmatrix}{{2\sigma_{\eta}^{2}R_{\eta}} + V_{\eta,\Phi}} & 0_{2 \times 2} \\0_{2 \times 2} & {{2\sigma_{\eta}^{2}R_{\eta}} + V_{\eta,\Phi}}\end{bmatrix}},{R_{\eta} = \begin{bmatrix}1 & {g\left( {T/2} \right)} \\{g\left( {T/2} \right)} & 1\end{bmatrix}}$where V_(Φ,n/n−L)=V_(Φ,n−L)+Q_(Φ)L is the covariance matrix of theindirect variable prediction error for L+1 steps, Q_(Φ) is thecovariance matrix of exciting noise of the indirect variable vector,${{B(S)} = \begin{bmatrix}{S^{T}A_{1}^{T}} \\{S^{T}A_{2}^{T}}\end{bmatrix}},\quad{{G\left( \Phi_{n} \right)} = \begin{bmatrix}{\Phi_{n}^{T}A_{1}} \\{\Phi_{n}^{T}A_{2}}\end{bmatrix}},$A₁ and A₂ are 4×(2m+1)-dimensioned approximation coefficient matrices asdescribed above, and m is a number of adjacent symbols taken intoaccount. A vector condition for TDMA symbols can be described by theequation S_(n)=A_(n)S_(n−1)+ξ_(n) where A_(n) is a shift matrix (or atransition matrix during the CDVCC) and ξ_(n) is noise with covariancematrix V_(ξ,n)=2Q_(ξ,n) which is a zero matrix during the CDVCC, thuswhen n is not in the CDVCC: $A_{n} = {{\begin{bmatrix}0 & 1 & 0 & \ldots & 0 \\0 & 0 & 1 & \ldots & 0 \\\ldots & \ldots & \ldots & \ldots & \ldots \\0 & 0 & 0 & \ldots & 1 \\0 & 0 & 0 & \ldots & 0\end{bmatrix}\quad Q_{n}} = \begin{bmatrix}0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\0 & 0 & \ldots & {1/2}\end{bmatrix}}$and when n relates to a known CDVCC symbol W_(n):$A_{n} = {{\begin{bmatrix}0 & 1 & 0 & \ldots & 0 \\0 & 0 & 1 & \ldots & 0 \\\ldots & \ldots & \ldots & \ldots & \ldots \\0 & 0 & 0 & \ldots & 1 \\0 & 0 & 0 & \ldots & w_{n}\end{bmatrix}\quad Q_{n}} = \begin{bmatrix}0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0\end{bmatrix}}$

Thus referring again to FIG. 3, the calculation unit 70 producesG(Φ_(n/n−L)), used in the first and third of Equations (9) and inEquation (8), from the indirect variable vectors Φ_(n) ^(A)and Φ_(n)^(B) tracked as described below, and the calculation units 76, 74, and72 produce the values of respectively the first, second, and third ofthe Equations (9). V_(ξ,n) supplied to the unit 74 is predetermined asindicated above, and V_(η,n) supplied to the unit 76 can also be fixedand predetermined or, as later described below, can be adaptivelychanged. The Kalman filter gain K_(s,n) is used by the multiplier 66 toproduce, with the other elements 60, 62, 64, and 68 of the Kalmanfilter, the equalizer output vector S_(Φn), from the signal samplesY_(n) ^(A) and Y_(n) ^(B) in accordance with Equation (8).

Referring now to FIG. 4, one form of the indirect variable tracking unit16A is illustrated, the unit 16B being similar and connections to italso being indicated in FIG. 4, together with one form of the frequencyoffset indirect variable estimation unit 22 and of the KΦ calculationunit 26. To some extent these units make use of similar calculations sothat they are closely inter-related and they are accordingly describedtogether below. As illustrated in FIG. 4, the indirect variable trackingunit 16A comprises signal combiners 80 and 82, multipliers 84, 86, 88,and 90, and a delay element 92. Although not shown separately in FIG. 4,the unit 16A is also supplied with the initial value Φ₀ ^(A) of theindirect variable vector Φ_(n) for synchronization by the unit 14A asdescribed above. The frequency offset indirect variable estimation unit22 comprises signal combiners 94, 96, and 98, multipliers 100 and 102, adelay element 104, and calculation units 106, 108, and 110. The KΦcalculation unit 26 comprises signal combiners 112 and 114, a delayelement 116, and calculation units 118, 120, 122, and 124.

The effect of frequency offset in conjunction with indirect variableerror ξ can be expressed by:Φ_(n) ^(A) =dF _(n)Φ_(n−1) ^(A)+ξ_(φ,n) ^(A)Φ_(n) ^(B) =dF _(n)Φ_(n−1) ^(B)+ξ_(φ,n) ^(B)  (10)dF _(n) =dF _(n−1 +ξ) _(dF,n)where dF_(n)≈ exp(j2πf_(of)T) and f_(of) is frequency offset. With anobservation model of the form:Y _(n) ^(A) =B(S _(n))Φ_(n) ^(A)+η_(n) ^(A) y _(n) ^(B) =B(S _(n))Φ_(n)^(B)+η_(n) ^(B)then if dF_(n−1) is estimated very accurately, substituting theestimates for the actual variable in Equation (10) produces a modelwhich does not depend upon this variable:Φ_(n) ^(A)=Φ_(n−1) ^(A)+ξ_(Φ,n) ^(A)Φ_(n) ^(B)=Φ_(n−1) ^(B)+ξ_(Φ,n) ^(B)  (10)and results in a filtering algorithm:Φ_(n) ^(A) =dF _(n−1)Φ_(n−1) ^(A) +K _(Φ,n)(Y _(n) ^(A) −B(S_(n))Φ_(n−1)^(A) dF _(n−1))  (11)Φ_(n) ^(B) =dF _(n−1)Φ_(n−1) ^(B) +K _(Φ,n)(Y _(n) ^(B) −B(S_(n))Φ_(n−1)^(B) dF _(n−1))whereK _(Φ,n) =V _(Φ,n/n−1) B(S_(n))′V _(v,n) ⁻¹ V _(ν,n) ⁻¹=(B(S _(n))V _(Φ,n/n−1) B(S _(n))′+2σ_(η) ² R _(η))⁻¹  (12)V _(Φ,n) =V _(Φ,n/n−1) −K _(Φ,n) [V _(Φ,n/n−1) B(S _(n))′]V _(Φ,n/n−1) =V _(Φ,n−1) +Q _(ξ,Φ)+ν_(dF,n−1)It can be appreciated here that the same Kalman gain matrix K_(Φ,n) isused for signals from the two antennas, thereby simplifying thefiltering algorithm and making its complexity independent of the numberof antennas.

It can be seen from FIG. 4 that the elements 80 to 92 of the trackingunit 16A are arranged to implement Equation (11) for the signal samplesY_(n) ^(A), the parameter dF_(n−1) being supplied from the output of thedelay element 104 and the parameter K_(Φ,n) being supplied from theoutput of the unit 124, to produce the tracked indirect variable vectorΦ_(n) ^(A) at the output of the signal combiner 82. The four Equations(12) are implemented in FIG. 4 respectively by the calculation units124, 122, and 120 and the elements 112 to 116.

For frequency offset estimation, the following approximated model isderived from the above:dF _(n) =dF _(n−1)+ξ_(dF,n)Y _(n) ^(A) =B(S _(n))Φ_(n−1) ^(A) dF _(n−1)+ν_(n) ^(A)Y _(n) ^(B) =B(S _(n))Φ_(n−1) ^(B) dF _(n−1)+ν_(n) ^(B)where ν_(n) ^(A) and ν_(n) ^(B) are equivalent observation noise whichtake into account estimation errors of the indirect variable vectorsΦ_(n−1) ^(A) and Φ_(n−1) ^(B) and have the same covariance matrixdefined by:V _(ν,n) =B(S _(n))V _(Φ,n/n−1) B(S _(n))′+2σ_(η) ²R_(η)

Then an indirect variable filtering algorithm for dF_(n) can be writtenin the form:

 dF _(n) =dF _(n−1) +K _(dF,n) ^(A)(Y _(n) ^(A) −B(S _(n))Φ_(n−1) ^(A)dF _(n−1))+K _(dF,n) ^(B)(Y _(n) ^(B) −B(S _(n))Φ_(n−1) ^(B) dF_(n−1))  (13)

whereK _(dF,n) ^(A)=ν_(dF,n)Φ_(n−1) ^(A) ′B(S _(n))′V _(ν,n) ⁻¹K _(dF,n) ^(B)=ν_(dF,n)Φ_(n−1) ^(B) ′B(S _(n))′V _(ν,n) ⁻¹  (14)ν_(dF,n)=1/[1/ν_(dF,n/n−1)+Φ_(n−1) ^(A) ′B(S _(n))′V _(ν,n) ⁻¹ B(S_(n))Φ_(n−1) ^(A)+Φ_(n−1) ^(B) ′B(S _(n))′V _(ν,n) ⁻¹ B(S _(n))Φ_(n−1)^(B)]ν_(dF,n/n−1)=ν_(dF,n−1) +Q _(ξ,dF)

Although Equations (14) appear to be very complex, they can beimplemented with low complexity because a large number of steps arealready otherwise performed. For example, the inverse matrix V_(ν,n) ⁻¹is used for calculation of K_(Φ,n), the differences in Equation (13) arethe same as those in Equation (11), and multiplications such asB(S_(n))Φ_(n−1) ^(A) have been used for difference calculations.

It can be seen from FIG. 4 that the four Equations (14) are implementedby the calculation units 108, 110, and 106 and the signal combiner 94respectively. The multipliers 100 and 102, signal combiners 96 and 98,and delay element 104 implement Equation (13).

Referring to FIG. 5, the hard limiter 24 is supplied with the vectorS_(Θ,n) from the output of the equalizer 18, and supplies the elementsS_(n+m) to S_(n−m) of this vector via respective ones of 2m+1 stages 130to produce hard limited elements which, with delayed versions thereofproduced by delay elements 132, constitute the elements of the vectorS_(n) that is supplied to the KΦ calculation unit 26, and in particularto the unit 118 as shown in FIG. 4. In addition, the hard limiter 24provides an output for the hard limited version of the element S_(n−m)to the demodulator 28, which operates in a well-known manner fordemodulating the π/4-shifted DQPSK signal. Each of the stages 130, asrepresented in FIG. 5 for two such stages, provides signal phaserotation, hard limiting, and derotation following the π/4-shifted DQPSKmodulation rules.

In order to optimize parameters for operation of the receiver asdescribed above, particular values can be selected. For example, thenumber 2m+1 of simultaneously estimated symbols in the equalizer 18 canbe selected as being 5 with m=2, and with L=2 as already indicated thenumber of symbols m+1+L used in the tracking units 16A and 16B is also5. The integration interval for the synchronization units can be 8 T,and in FIG. 4 Q_(ξ,Φ) can be (diag (10⁻⁴*[2 1 0.5 0.5]), and Q_(ξ,dF)can be 2.5 *10⁻⁵ In addition, a fixed value of SNR, for example 17 dB,can be used for synthesizing the above algorithms, as the actualsignal-to-noise and interference ratio may be unknown.

The receiver as described above is intended to provide an optimumperformance in the presence of noise. However, in the presence ofco-channel interference, the performance of the receiver can bedegraded. In order to reduce or avoid such degradation, the receiver canalso include the interference correlation matrix (ICM) estimation unit30 shown in dashed lines in FIG. 1. This provides an adaptive control ofthe matrix V_(η,n) which is supplied to the linear indirect variableequalizer 18, so that interference cancellation is also achieved by theoperation of the equalizer as described above.

An analysis can be carried out in a similar manner to that describedabove in relation to the operation of the tracking units, but in respectof the information symbols S_(i) in the TDMA time slot rather than thesynchronization symbols, from which it can be determined that the noisecovariance matrix V_(η,n) provides interference cancellation based ondifferences of estimated values ε_(i) ^(A)=Y_(i) ^(A)−G(Φ_(i) ^(A))S_(i)and ε_(i) ^(B)=Y_(i) ^(B)−G(Φ_(i) ^(B))S_(i) which are alreadydetermined (Equation (8) above, using a slightly different notation) inthe operation of the Kalman filter as described above. As illustrated inFIG. 1, these differences are supplied from the tracking units 16A and16B to the ICM estimation unit 30 to enable estimation of the matrixV_(η,n). This matrix is determined by:$V_{\eta} = {{2R_{\eta}^{AB}} = {2\begin{bmatrix}{\sigma_{A}^{2}R_{\eta}} & {r_{AB}^{\prime}R_{\eta}} \\{r_{AB}R_{\eta}} & {\sigma_{B}^{2}R_{\eta}}\end{bmatrix}}}$where σ_(A) ² and σ_(B) ² are unknown variances (real variables), r_(AB)is an unknown correlation coefficient (complex variable), and R_(η) isthe known covariance matrix already specified above.

FIG. 6 illustrates one form of the ICM estimation unit 30, in which theunknowns σ_(A) ², σ_(B) ² and r_(AB) are each averaged over a desirednumber NA of samples by respective delay lines 140 and summing units142, the outputs of which are supplied to a calculation unit 144 todetermine the covariance matrix V_(η) in accordance with the aboveequation. The unit 30 also includes multipliers 146, 148, 150, 152, and154, and transpose units 156 and 158, which serve to produce theelements of the matrix as inputs to the delay lines 140 for averaging.Thus it can be seen that this adaptive operation of the receiver addsvery little complexity to the receiver, but can substantially improvethe performance of the receiver in the presence of co-channelinterference.

Although a dual antenna embodiment of the invention has been describedabove in detail, it should be appreciated that the invention is notlimited in this respect, and it may also be applied to a single antennareceiver as illustrated in FIG. 7. Thus as shown in FIG. 7, a singleantenna 160 is coupled via a receiver front end unit 162 whose outputsignal samples Y_(n) are supplied to an indirect variablesynchronization unit 164, an indirect variable tracking unit 166, and alinear indirect variable equalizer 168. The synchronization unit 164provides an initial synchronization vector Φ₀ to the tracking unit 166,no frame alignment being required because in this case there is only onesignal path. The tracking unit 166 provides a tracked vector Φ_(n), andthis is equalized by the equalizer 168 to produce a resulting signal fordemodulation by a demodulator 170. It can be appreciated that the units164, 66, and 168 in the receiver of FIG. 1 can use similar principles tothose described above in order to provide improved single-antennareceiver performance through the use of indirect variables for all ofthe signal processing in the receiver prior to the demodulator.

It can be appreciated that although as described above the frequencyoffset estimation unit 22 is provided as is preferred to compensate forfrequency offsets, which may be due to local oscillator frequencyvariations and, especially, due to Doppler effects, in other embodimentsof the invention this unit can be omitted.

In addition, although the description above refers to, and the drawingsillustrate, particular units such as calculation units, signalcombiners, multipliers, delay elements, and so on, it should beappreciated that in practice the functions of all of these units canconveniently be carried out by one or more digital signal processors orapplication-specific integrated circuits.

Thus although particular embodiments of the invention have beendescribed above, it can be appreciated that these and numerous othermodifications, variations, and adaptations may be made without departingfrom the scope of the invention as defined in the claims.

1. A method of processing samples of a received signal to produce ademodulated signal, comprising the steps of: representing an impulseresponse matrix for the received signal using a plurality of indirectvariables of a linear complex vector; synchronizing to the receivedsignal samples in dependence upon the indirect variables; tracking theindirect variables for successive received signal samples; equalizingthe successive received signal samples in dependence upon the trackedindirect variables; and producing the demodulated signal in response tothe equalized received signal samples; wherein the step of synchronizingto the received signal samples comprises matched filtering the receivedsignal samples to produce the plurality of indirect variables, anddetermining a maximum of a function of the indirect variables todetermine synchronization.
 2. A method as claimed in claim 1 wherein thereceived signal is a signal of a TDMA communications system.
 3. A methodas claimed in claim 1 wherein there are four indirect variables and saidfunction is a function of only two of the indirect variables.
 4. Amethod as claimed in claim 1 wherein the step of tracking the indirectvariables for successive received signal samples comprises recursivelyfiltering initial values of the indirect variables, established duringthe synchronizing step, in dependence upon the successive receivedsignal samples.
 5. A method as claimed in claim 4 wherein said indirectvariables are produced and tracked individually in respect of samples ofa received signal from each of two spaced antennas, and received signalsamples from the two antennas are combined and equalized in dependenceupon a combination of the indirect variables in respect of the twoantennas.
 6. A method as claimed in claim 1 wherein the step of trackingthe indirect variables for successive received signal samples comprisesa step of estimating frequency offset in dependence upon the successivereceived signal samples.
 7. A method as claimed in claim 6 wherein saidindirect variables are produced and tracked individually in respect ofsamples of a received signal from each of two spaced antennas, andreceived signal samples from the two antennas are combined and equalizedin dependence upon a combination of the indirect variables in respect ofthe two antennas.
 8. A method as claimed in claim 1 wherein the step ofequalizing the successive received signal samples comprises adaptivelychanging an equalizer parameter in dependence upon tracking errors forsuccessive received signal samples to reduce co-channel interference inthe received signal.
 9. A method as claimed in claim 8 wherein saidindirect variables are produced and tracked individually in respect ofsamples of a received signal from each of two spaced antennas, andreceived signal samples from the two antennas are combined and equalizedin dependence upon a combination of the indirect variables in respect ofthe two antennas.
 10. A method as claimed in claim 1 wherein saidindirect variables are produced and tracked individually in respect ofsamples of a received signal from each of two spaced antennas, andreceived signal samples from the two antennas are combined and equalizedin dependence upon a combination of the indirect variables in respect ofthe two antennas.
 11. An apparatus for producing a demodulated signalfrom samples of a received signal, comprising: a synchronization unitresponsive to the received signal samples for producing a linear complexvector comprising a plurality of indirect variables having initialvalues corresponding to a synchronized state; a tracking unit responsiveto the initial values of the indirect variables and to the receivedsignal samples to produce tracked values of the indirect variables forsuccessive received signal samples; an equalizer responsive to thetracked values of the indirect variables to equalize successive receivedsignal samples; a feedback path from the equalizer to the tracking unitto facilitate producing the tracked values of the indirect variables bythe tracking unit; and a demodulator responsive to the equalizedreceived signal samples to produce a demodulated signal.
 12. Theapparatus as claimed in claim 11 wherein the synchronization unitcomprises a plurality of finite impulse response filters for matchedfiltering of the received signal samples to produce the plurality ofindirect variables.
 13. The apparatus as claimed in claim 11 wherein thetracking unit comprises a recursive filter for recursively filtering theindirect variables in dependence upon the successive received signalsamples.
 14. The apparatus as claimed in claim 13 further comprisingrespective synchronization and tracking units for samples of a receivedsignal from each of two spaced antennas, wherein the equalizer isresponsive to the tracked indirect variables for both antennas tocombine and equalize the received signal samples from the two antennas.15. The apparatus as claimed in claim 11 further comprising a frequencyoffset estimator coupled to the tracking unit for modifying the trackingof the indirect variables in accordance with estimated frequency offsetin dependence upon the successive received signal samples.
 16. Theapparatus as claimed in claim 15 further comprising respectivesynchronization and tracking units for samples of a received signal fromeach of two spaced antennas, wherein the equalizer is responsive to thetracked indirect variables for both antennas to combine and equalize thereceived signal samples from the two antennas.
 17. The apparatus asclaimed in claim 11 further comprising a unit, responsive to trackingerrors determined by the tracking unit for successive received signalsamples, for estimating an interference correlation matrix to adaptivelychange a parameter of the equalizer to reduce co-channel interference inthe received signal.
 18. The apparatus as claimed in claim 17 furthercomprising respective synchronization and tracking units for samples ofa received signal from each of two spaced antennas, wherein theequalizer is responsive to the tracked indirect variables for bothantennas to combine and equalize the received signal samples from thetwo antennas.
 19. The apparatus as claimed in claim 11 furthercomprising respective synchronization and tracking units for samples ofa received signal from each of two spaced antennas, wherein theequalizer is responsive to the tracked indirect variables for bothantennas to combine and equalize the received signal samples from thetwo antennas.